An efficient method is developed for plunger thermal cycle analysis in repeated forming process of the TV glass. The plunger undergoes temperature fluctuation during a cycle due to the repeated contact and separation from the glass, which attains a cyclic steady state having same temperature history at every cycle. Straightforward analysis of this problem brings about more than 80 cycles to get reasonable solution, and yet hard to setup stopping criteria due to extremely slow convergence. An exponential fitting method is proposed to overcome the difficulty, which finds exponential function to best approximate temperature values of 3 consecutive cycles, and new cycle is restarted with the fitted value at infinite time. Numerical implementation shows that it reduces the number of cycles dramatically to only 6-18 cycles to reach convergence within 10 accuracy. A system for the analysis is constructed, in which the thermal analysis is performed by commercial software ANSYS, and the fitting of the result is done by IMSL library. From the parametric studies, one reveals some important facts that although the plunger cooling or the glass thickness is increased, its counter part in contact is not much affected, duo to the low thermal conductance of the glass.